Character motivation simply means what drives the character to do what he/she does.
For example, in To Kill a Mockingbird, Jem believes he has discovered what motivates Boo Radley to stay in his house, away from everyone else. In Chapter 23, Aunt Alexandra claims that the Cunninghams are trash and this is why Scout should not associate with Walter. Before Scout can carry on the argument, Jem pulls her away. Jem concludes that someone might not want to live in a town where he/she is judged by family history and income. He says:
I think I’m beginning to understand why Boo Radley’s stayed shut up in the house all this time… it’s because he wants to stay inside.
At the beginning of the same chapter, it is revealed why Atticus doesn't brag about his shooting ability and why he allows Bob Ewell to get away with spitting on him and insulting him. Atticus says, "The man had to have some kind of comeback, his kind always does. So if spitting in my face and threatening me saved Mayella Ewell one extra beating, that’s something I’ll gladly take." Atticus is motivated by an uncompromising moral belief. He always tries to do and say the right thing. He doesn't brag. He always tries to think how the other person thinks and feels.
In Chapter 15, Jem and Scout refuse to go home when they approach Atticus while he guards the courthouse. Jem is particularly defiant. Scout realizes Jem might know something she doesn't. She thinks, "I was getting a bit tired of that, but felt Jem had his own reasons for doing as he did . . . " Jem feared for Atticus' safety. He assumed nothing would happen as long as the three children stayed.
In Chapter 27, after the trial and Tom's death, Bob Ewell is still being a nuisance. He follows Helen on her way to and from work, harassing her. Mr. Deas puts a stop to it. Even though Mr. Ewell got what he wanted in court, he was back to his old, pathetic life. Atticus adds, "He thought he’d be a hero, but all he got for his pain was… was, okay, we’ll convict this Negro but get back to your dump." Bob Ewell is always looking to blame someone else for his lot in life.
In Chapter 3, Calpurnia scolds Scout for making fun of Walter. Calpurnia and Atticus are the primary role models/parental figures who teach Scout and Jem not to judge people. This is why she says, "Don’t matter who they are, anybody sets foot in this house’s yo‘ comp’ny, and don’t you let me catch you remarkin’ on their ways like you was so high and mighty!"
Throughout the novel, Scout is often motivated by curiosity, which Atticus encourages. She is so open-minded that she sees no problem with acting more like a boy than a girl. Scout is also very perceptive for her age. During the trial, she understands why Mayella would lie in court. She understands why Atticus is sympathetic to Mayella's situation. In Chapter 19, she thinks:
As Tom Robinson gave his testimony, it came to me that Mayella Ewell must have been the loneliest person in the world. She was even lonelier than Boo Radley, who had not been out of the house in twenty-five years.